Branching Random Processes

Abstract

Consider a set of objects (for example, molecules) of n types T ₁, T ₂,…,T _n and assume that with probability, during the time interval (t ₁,t ₂ ) one object of type T _k . turns into the set consisting of α₁ objects of the first type, α₂ objects of the second type, α _i , objects of type i, etc. A random process consisting of this kind of transformation is called a branching process if the probabilities are uniquely determined by the times t ₁ < t ₂, the number k of the original type, k = 1, 2,…, n, and the n-dimensional vector α = (α₁,α₂,…, α _n ) with integer coefficients, α _i = 0,1,2….

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Dokl. Akad. Nauk SSSR56:1 (1947), 7-10.